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arXiv:1603.01967 · Physical Review Letters

Simultaneous Precision Gravimetry and Magnetic Gradiometry with a Bose-Einstein Condensate: A High Precision, Quantum Sensor

Kyle S. Hardman, P. J. Everitt, Gordon McDonald, Manju Perumbil, P. B. Wigley, M. A. Sooriyabandara, C. C. N. Kuhn, J. E. Debs, J. D. Close, Nicholas P. Robins

Published Sep 21, 2016• 131 citations
arXivHTMLPDF

Abstract

A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A $5\ifmmode\times\else\texttimes\fi{}1{0}^{6}\text{ }\text{ }\mathrm{atom}$ $F=1$ spinor condensate of $^{87}\mathrm{Rb}$ is released into free fall for up to 750 ms and probed with a $T=130\text{ }\text{ }\mathrm{ms}$ Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states $|{m}_{f}=1,0,\ensuremath{-}1⟩$, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of $\mathrm{\ensuremath{\Delta}}g/g=1.45\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and the magnetic field gradient to a precision of $120\text{ }\mathrm{pT}/\mathrm{m}$.

DOI
10.1103/physrevlett.117.138501

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A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A 5\ifmmode×\else\texttimes\fi106  atom5\ifmmode\times\else\texttimes\fi{}1{0}^{6}\text{ }\text{ }\mathrm{atom}5\ifmmode×\else\texttimes\fi106  atom F=1F=1F=1 spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb is released into free fall for up to 750 ms and probed with a T=130  msT=130\text{ }\text{ }\mathrm{ms}T=130  ms Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states ∣mf=1,0,\ensuremath−1⟩|{m}_{f}=1,0,\ensuremath{-}1⟩∣mf​=1,0,\ensuremath−1⟩, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of \ensuremathΔg/g=1.45\ifmmode×\else\texttimes\fi10\ensuremath−9\mathrm{\ensuremath{\Delta}}g/g=1.45\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\ensuremathΔg/g=1.45\ifmmode×\else\texttimes\fi10\ensuremath−9 and the magnetic field gradient to a precision of 120 pT/m120\text{ }\mathrm{pT}/\mathrm{m}120 pT/m.
A precision inertial sensor based on the interference of matter waves has been designed and implemented. The apparatus is capable of producing both cold thermal and ultracold Bose-Einstein condensate (BEC) atomic ensembles as the inertial test mass. BECs of up to 5x10^6 Rubidium 87 atoms with an effective temperature of 50nK are produced every 13 seconds using a combination of two and three dimensional magneto-optical traps (2D and 3D MOT) and evaporative cooling in a hybrid magnetic-quadrupole and crossed optical dipole trap. The atomic cloud is then propagated through a vertically oriented Mach-Zehnder interferometer utilizing Bragg diffraction beam splitters. An 2.6m drop tube allows for up to 750ms of free fall and interferometer times of up to 250ms. The drop has four regions of imaging corresponding to 0, 25, 220, 530, and 750ms of expansion. Standard absorption imaging is used for the upper two imaging regions and frequency modulation imaging (FMI) is used for the lower regions. FMI exhibits near atom-shot noise limited signal-to-noise of 948 on a 1x10^6 atom cloud. The inertial reference is provided by the Bragg beam retro-reflector which is suspended via a geometric anti-spring passive vibration isolation system providing 65 dB of isolation at 70 Hz. Prior to the first interferometer pulse the ensemble is placed into a spin superposition of the |F=1> ground state manifold using horizontal co-propagating Raman beams. The three internal spin states remain orthogonal throughout the interferometer sequence resulting in three simultaneous interferometer with separable magnetic gradient and gravitational acceleration signals. The effects of meanfield energy on the interferometric phase uncertainty is explored under current trap conditions. It is found that 30 ms of free expansion prior to the first beam splitter decreases the internal energy such that the expected meanfield phase noise is below 1mrad. No significant decrease in the interferometer contrast is observed for all available T, whereas a thermal test mass interferometer of equivalent longitudinal temperature produces no interference at interferometer times > 100ms. A direct comparison of test mass spatial coherence length in an optically transversely confined interferometer is investigated. The visibility and contrast of a BEC and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100%, nearly independent of p pulse efficiency, while thermal sources have fringe visibilities limited to the p pulse efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond that of the thermal source. A BEC test mass is used for the simultaneous precision measurement of gravity and magnetic field gradients. An 8 hour data run of a 130ms interferometer shows good agreement between the interferometer output and a theoretical model of the solid earth tides. The residual of the theoretical model and the experimental data show a 1000 run precision of dg/g = 1.45x10^9 corresponding to a phase noise of 3.8mrad. The integrated phase noise of the apparatus shows a sensitivity to magnetic field gradients of 120pT/m. By varying the central spatial position of a 40ms interferometer the magnetic field gradient along a portion of the drop tube is measured.
Cold atom free-fall interferometers now realize state-of-the-art precision inertial sensors, opening perspectives towards embedded devices for applications and fundamental physics tests on earth and in space. The acceleration of gravity can be measured in a stimulated Raman transition interferometer where the acceleration under gravity of a cloud of freely falling atoms is sensed by three Raman pulses allowing to split, reflect and interfere atomic wave packets [1]. The gravimeter developped at SYRTE allows to measure the acceleration of gravity at state-of-the-art performances compared to the best classical absolute gravimeters, with a sensitivity of 2×10−8g over 1s and an exactitude of 5×10−9 g [2]. This exactitude is currently limited by wavefront aberrations of the lasers, sampled by residual transverse trajectories of the molasse-cooled cloud over the free fall. Unbalanced transverse trajectories will also bias the measurement due to Coriolis effect [3]. We will investigate the use of a colder atom source to reduce these systematic effects, by implementing Bose-Einstein condensation of the initial cloud, allowing both better position control and better focusing of our source.
We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate 87Rb^{87}\mathrm{Rb}87Rb spin-1 condensates in free fall and infer their relative Larmor phase, and thus the differential magnetic-field strength, with a common-mode phase noise suppression exceeding 50dB50\phantom{\rule{0.28em}{0ex}}\mathrm{dB}50dB. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure in vacuo the magnetic-field-gradient tensor of ambient and applied magnetic fields with a nominal precision of $0.30\phantom{\rule{0.28em}{0ex}}\mathrm{nT}\phantom{\rule{0.16em}{0ex}}{\mathrm{mm}}^{\ensuremath{-}1}$ and a sensor volume of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.28em}{0ex}}{\mathrm{mm}}^{3}$. We predict a spin-projection noise-limited magnetic energy resolution of order $\ensuremath{\sim}10\ensuremath{\hbar}$ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle of current BEC experiments.
We present a precision gravimeter based on coherent Bragg diffraction of freely falling cold atoms. Traditionally, atomic gravimeters have used stimulated Raman transitions to separate clouds in momentum space by driving transitions between two internal atomic states. Bragg interferometers utilize only a single internal state, and can therefore be less susceptible to environmental perturbations. Here we show that atoms extracted from a magneto-optical trap using an accelerating optical lattice are a suitable source for a Bragg atom interferometer, allowing efficient beamsplitting and subsequent separation of momentum states for detection. Despite the inherently multi-state nature of atom diffraction, we are able to build a Mach–Zehnder interferometer using Bragg scattering which achieves a sensitivity to the gravitational acceleration of Δ g / g = 2.7 × 10 −9 with an integration time of 1000 s. The device can also be converted to a gravity gradiometer by a simple modification of the light pulse sequence.
We present a cold-atom gravimeter operating with a sample of Bose-condensed 87{}^{87}87Rb atoms. Using a Mach-Zehnder configuration with the two arms separated by a two-photon Bragg transition, we observe interference fringes with a visibility of ($83\ifmmode\pm\else\textpm\fi{}6$)% at T=3T=3T=3 ms. We exploit large momentum transfer (LMT) beam splitting to increase the enclosed space-time area of the interferometer using higher-order Bragg transitions and Bloch oscillations. We also compare fringes from condensed and thermal sources and observe a reduced visibility of ($58\ifmmode\pm\else\textpm\fi{}4$)% for the thermal source. We suspect the loss in visibility is caused partly by wave-front aberrations, to which the thermal source is more susceptible due to its larger transverse momentum spread. Finally, we discuss briefly the potential advantages of using a coherent atomic source for LMT, and we present a simple mean-field model to demonstrate that with currently available experimental parameters, interaction-induced dephasing will not limit the sensitivity of inertial measurements using freely falling, coherent atomic sources.